Simplify ( square root of a^3)( square root of a^5)

$(\sqrt{a^{3}}) (\sqrt{a^{5}})$

Step 1

Factor out $a^{2}$ .

$\sqrt{a^{2} a} \sqrt{a^{5}}$

Step 2

Pull terms out from under the radical.

$a \sqrt{a} \sqrt{a^{5}}$

Step 3

Rewrite $a^{5}$ as ${(a^{2})}^{2} a$ .

Factor out $a^{4}$ .

$a \sqrt{a} \sqrt{a^{4} a}$

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$a \sqrt{a} \sqrt{{(a^{2})}^{2} a}$

Step 4

Pull terms out from under the radical.

$a \sqrt{a} (a^{2} \sqrt{a})$

Step 5

Multiply $a$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$a^{2} a \sqrt{a} \sqrt{a}$

Multiply $a^{2}$ by $a$ .

Raise $a$ to the power of $1$ .

$a^{2} a^{1} \sqrt{a} \sqrt{a}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{2 + 1} \sqrt{a} \sqrt{a}$

Add $2$ and $1$ .

$a^{3} \sqrt{a} \sqrt{a}$

Step 6

Multiply $a^{3} \sqrt{a} \sqrt{a}$ .

Raise $\sqrt{a}$ to the power of $1$ .

$a^{3} ({\sqrt{a}}^{1} \sqrt{a})$

Raise $\sqrt{a}$ to the power of $1$ .

$a^{3} ({\sqrt{a}}^{1} {\sqrt{a}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{3} {\sqrt{a}}^{1 + 1}$

Add $1$ and $1$ .

$a^{3} {\sqrt{a}}^{2}$

Step 7

Rewrite ${\sqrt{a}}^{2}$ as $a$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a}$ as $a^{\frac{1}{2}}$ .

$a^{3} {(a^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a^{3} a^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$a^{3} a^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a^{3} a^{\frac{2}{2}}$

Rewrite the expression.

$a^{3} a^{1}$

Simplify.

$a^{3} a$

Step 8

Multiply $a^{3}$ by $a$ by adding the exponents.

Multiply $a^{3}$ by $a$ .

Raise $a$ to the power of $1$ .

$a^{3} a^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{3 + 1}$

Add $3$ and $1$ .

$a^{4}$

Simplify ( square root of a^3)( square root of a^5)

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